# Stochastic Time-Dependent DFT with Optimally Tuned Range-Separated Hybrids: Application to Excitonic Effects in Large Phosphorene Sheets

## TL;DR

This paper introduces a stochastic time-dependent DFT method with optimally tuned range-separated hybrids that efficiently calculates excitonic optical spectra in large phosphorene sheets, matching experimental results.

## Contribution

It presents a novel stochastic approach to TDDFT with non-local exchange, enabling efficient and accurate excitonic spectra calculations for large 2D materials.

## Key findings

- Accurately reproduces experimental optical spectra.
- Scales quadratically with the number of electrons.
- Demonstrates efficiency on large phosphorene sheets with up to 1958 electrons.

## Abstract

We develop a stochastic approach to time-dependent DFT with optimally-tuned range-separated hybrids containing non-local exchange, for calculating optical spectra. The attractive electron-hole interaction, which leads to the formation of excitons, is included through a time-dependent linear-response technique with a non-local exchange interaction which is computed very efficiently through a stochastic scheme. The method is inexpensive and scales quadratically with the number of electrons, at almost the same (low) cost of time dependent Kohn-Sham (TDKS) with local functionals. Our results are in excellent agreement with experimental data and the efficiency of the approach is demonstrated on large finite phosphorene sheets containing up to 1958 valence electrons.